CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:    A Framework for Variational Grid Generation with Matrix Norms
 

SPEAKER: Patrick M. Knupp, Ecodynamics Research Associates, Albuquerque, NM

DATE:    Friday, February 23, 1996

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    noon - 1 pm



ABSTRACT

A general approach to the construction of functionals to be used for 
variational grid generation of structured grids, in which the Jacobian matrix 
and matrix norms play a central role, is introduced.  The theory focuses on 
the Jacobian matrix because all first-order geometric properties of a 
structured grid---including the direction of coordinate lines---are represented
by this matrix.   If directional control is not needed, the metric tensor 
can be used in place of the Jacobian matrix.   We show how grids with 
desired properties can be generated by minimizing functionals that require 
combinations of weight matrices with the Jacobian matrix or metric tensor to 
take certain basic forms.  Most of the well-known grid generators fit within 
this framework, and new ones, which directly control the Jacobian matrix, 
are proposed.  The first part of the talk will be a brief introduction to
structured grid generation, largely based on the book `The Fundamentals of
Grid Generation' by myself and Stanly Steinberg.